For the piecewise function below, which of the following statements are true?
Please help will give brainlist if correct!
Answers
The correct option is (b) i.e. f(0) > f(2).
What is Domain?
The entire range of independent variable values is the domain of a function. In straightforward terms, this definition means The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
We have,
f(x) = (x+2)^2 - 1 , -4 ≤ x ≤ 0
-x + 1 , 0 ≤ x ≤ 2
5/2 log ( -x +5) - 1 , 2 < x < 5
Now, f(0) = (x+2)^2 - 1
= (0+2)^2 - 1
= 4 - 1 = 3
Similarly, f(2) = - x +1
= - 2 + 1
= - 1.
Hence, f(0) > f(2) because 3 > -1.
∴ The correct option is (b).
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Related Questions
In 1970, 83% of 30-year-olds in a country earned more than their parents did at age 30(adjusted for inflation). In 2014, only 46% of 30-year-olds in the same country earnedmore than their parents did at age 30. Complete parts a to d below.(a) What is the probability a randomly selected 30-year-old in 1970 earned more thanhis or her parents at age 30?The probability is(Round to four decimal places as needed.)(b) What is the probability that two randomly selected 30-year-olds in 1970 earnedmore than their parents at age 30?The probability is a(Round to four decimal places as needed.)(c) What is the probability that out of ten randomly selected 30-year-olds in 1970, atleast one did not earn more than his or her parents at age 30?The probability is(Round to four decimal places as needed.)(d) What is the probability that out of ten randomly selected 30-year-olds in 2014, atleast one did not earn more than his or her parents at age 30?The probability is(Round to four decimal places as needed.)
Answers
Part a) If in 1970 the 83% of 30-year-olds earned more than their parents, then if we choose at random one 30-year-old person the probability that he/she earned more than his/her parents when they were 30 years old is 0.8300.
Part b) The probability of two randomly selected 30-year-olds in 1970 earned more than their parents at age 30 is 0.83*0.83= 0.6889.
Part c) For this part we use binomial probability. The probability of interest is equal to the probability that at least 9 earned more than their parents. The probability that at least 9 earned more than their parents is:
\(\begin{gathered} P(x\ge9)=P(x=9)+P(x=10) \\ =\frac{10!}{(10-10)!10!}(0.83)^{10}\cdot(1-0.83)^{10-10}+\frac{10!}{(10-9)!9!}(0.83)^9\cdot(1-0.83)^{10-9} \\ =0.83^{10}+10(0.83)^9(0.17) \end{gathered}\)computing we get 0.4730.
Part d) Solving similarly as part c) but considering that the probability for the year 2014 instead of the one for 1970 we get:
\(\begin{gathered} P(x\ge9)=P(x=9)+P(x=10) \\ =(0.46)^{10}+10(0.46)^9(0.54) \end{gathered}\)computing we get 0.0054.
A set of weights includes a 10lb barbell and 4 pairs of weight plates. Each pair of plates weighs 30lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates can be represented by f(x)=30x+10What is the range of the function?A) {10, 40, 70, 100, 130B) {0, 1, 2, 3, 4}C) {0, 2, 4}D) {10, 70, 130}
Answers
The range of the function is all of the values (y) the function can take for every input (x).
In this case, we have that the function is f(x) = 30x + 10, for the explained reasons in the question.
x is pairs of plates added to the barbell.
Then, we have:
1. The function with the barbell with no pair of plates is:
f(0) = 30(0) + 10 = 10
2. With one pair of plates:
f(1) = 30(1) + 10 = 40
3. With two pairs of plates:
f(2) = 30(2) + 10 = 60 + 10 = 70.
Then, we have:
f(3) = 30(3) + 10 = 90 + 10 = 100.
f(4) = 30(4) + 10 = 120 + 10 = 130.
Therefore, the range of the function (the total weight of the barbell) is option A {10, 40, 70, 100, 130}.
Which ratio is the same as 2/3?
Answers
Answer:
The ratio 2 : 3 is the same as the ratio of 6 : 15.
I dont know if that the same at what you refer.
Answer:
4/6, 6/9, 8/12, 10/15
Step-by-step explanation:
Basically you keep adding 3 to the denominator, and multiply the numerator by 2
Find the numbers with the following property three times the sum of four and a number is less than seven times the same number
Answers
Let's represent the number with the variable "x". According to the given property, we can write the following equation:
3(x + 4) < 7x
Now, let's solve this inequality to find the range of numbers that satisfy the property.
3x + 12 < 7x
Subtract 3x from both sides:
12 < 4x
Divide both sides by 4 (since the coefficient of x is 4):
3 < x
So, the range of numbers that satisfy the given property is x > 3.
Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:
According to the problem, we know that:
3(4 + x) < 7x
Simplifying:
12 + 3x < 7x
Subtracting 3x from both sides:
12 < 4x
Dividing both sides by 4:
3 < x
So the number we're looking for must be greater than 3.
What is the solution to this system of equations?
8a−4b=20
5a−8b=62
a=
b=
Answers
Answer:
Hello there, I think this is the answer
a = - 2
b = - 9
Consider the following system of two linear equations:
3y + 2x = 15
x – y = 0
Select the graph that correctly displays this system of equations and point of intersection.
Answers
The answer is x = 3 y=3. This can be solved by reorganising the equation 2x + 3y = 15, x-y=0.
What is Multiplication Zero Property?This property is true for all real numbers, including integers, fractions, decimals, and any other real number. The Multiplication Zero Property states that the product of any number and zero is equal to zero.
Reorganising the equation:
2x + 3y = 15
x-y=0
To find the solution, multiply both parts of the equation by a multiplier, as in 2x+3y=15.
2(x-y)=0 x 2
Utilize the multiplicative distributional rule.
2x+3y=15
2x-2y=0 x 2
Application of the Multiplication Zero Property
2x+3y=15
2x-2y=0
Separate the two formulas: 2x+3y-(2x-2y)=15-0
2x+3y-2x+2y=15
Take the parentheses off
3+2=15
Expressions combined: 5y=5
Multiply both sides of the equation by the value of the variable: y = 15/5
Take out the joining piece. y=3
Substitute 0 for 2x-2x-2x in one of the computations.
2x-6=0 is used to determine the product.
In the calculation, 6 should be shifted to the left: 2x=6
Add the variable's value to both ends of the equation, then subtract it:
x = 6/2
Take out the intermediary: 2 = 3
The answer is x = 3 y=3.
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STD 10
maths
If the ratio of areas of two similar triangles is 9 : 4, then the ratio of its corresponding sides is .
(a) 9 : 4 (b) 4 : 9 (c) 3 : 2 (d) 81 : 16
Answers
Answer:
The answer is c
Step-by-step explanation:
If the area of the two triangles are similar, then Area of ∆ 1 : Area of ∆ 2 =
(Side of ∆ 1)² : (Side of ∆ 2)²
____________________________
Since the area of each triangle is equal to the corresponding side squared.
Area of ∆ = (Side of ∆)² →
√(Area of ∆) = Side of ∆ →
Side of ∆ = √(Area of ∆).
Therefore:
9 : 4 → √9 : √4 = 3 : 2
75% of students is blank of 20 students
Answers
Explanation: multiply 20 by .75
Answer:
Step-by-step explanation:
Solve for <2.
499
62 = [?]
44/42
![Solve for <2.49962 = [?]44/42](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/HuHcSrtaFWuNxrZgpRwFBSNc7XfhKVls.png)
Answers
Answer:
Solution given'
<2+90+49=180°[sum of interior angle of a triangle]
<2=180-139
<2=41°
What’s the area? Please help!!
Answers
The area of the triangle can be found by A = 1/2bh
So the area will be 1/2 times (6+14+6= 26) 26 times 21
The area of the triangle will be 273 ft^2
The area of the square will be A=lxh
So the area will be 14 times 14
So the area of the square will be 196 ft ^2
We then add the area of both shapes together to get the total area
273 + 196 = 469 ft^2
9514 1404 393
Answer:
469 square yards
Step-by-step explanation:
The area of the triangle is ...
A = 1/2bh
A = 1/2(6+14+6)(21) = 273
The area of the square is ...
A = s^2 = 14^2 = 196
The total area of the figure is the sum of the parts.
273 +196 = 469 . . . square yards
An element with a mass of 570 grams decays by 26.7% per minute. To the nearest minute, how long will it be until there are 40 grams of the element remaining?
Answers
Answer: x ≈ 9
Step-by-step explanation:
Near the end of the picture 8.553364=x
x ≈ 9
What is 48 square feet in square meters
Answers
Answer: 4.45935
Step-by-step explanation: 1 Square foot (sqft) is equal to 0.09290304 square meter (sqm). For example, to convert 100 square feet to square meters, multiply 100 by 0.09290304, that makes 9.290304 sqm is 100 sqft. Hope this helps.
Thi has taken four math tests. She scored 96 on her
first test. For each of the next three tests, the table shows the
change in score from the previous test. Find the mean of
the changes.
Answers
Answer:
84.5
Step-by-step explanation:
1: 96 - 13 to get difference = 83
2: 83 - 5 = 78
3: 78 + 3 = 81
4: (83 + 78 + 81 + 93) / 4 = 84.5
31-+=16
28+b=50
33+c=54
52-n+=24
Answers
The solution to the equations are b = 15, b = 22, c = 21 and n = 28
How to determine the solution to the equationsFrom the question, we have the following equations that can be used in our computation:
31 - b = 16
28 + b = 50
33 + c = 54
52 - n = 24
Next, we collect the like terms in each of the equation
This gives
b = 31 - 16
b = 50 - 28
c = 54 - 33
n = 52 - 24
Lastly, we evaluate the like terms
b = 15
b = 22
c = 21
n = 28
The above are the solutions to the equations
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Question
Solve the following equations:
31 - b = 16
28 + b = 50
33 + c = 54
52 - n = 24
If ∆HBN~∆LYR, find the value of x.
Answers
Answer:
x=6
Step-by-step explanation:
32-21 = 11
28-11 = 17
17-11 = 6
x=6
Which transformation results in the function?
Answers
The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,
How to describe the transformation from the parent function?From the question, we have the following functions that can be used in our computation:
f(x) = x²
g(x) = (4x)²
Mathematically, these equations can be represented as
g(x) = f(4x)
The above equations implies that, we have the transformation to be:
The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4
Hence, the transformed function is (a)
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NO LINKS PLS
The ratio of hot dogs to hamburgers on a barbeque table is 5:4. If there are 36 hamburgers on the table then how many hot dogs must be there?
Answers
Step-by-step explanation:
let the ratio be x
then, 5x, 4x is the ratio of hotdog and hamburger
According to question,
5x+3x=36
8x=36
x=36÷8
x=4
therefore, no, of hotdogs are= 5x
=5×4
=20
The density of oxygen is 1.429*10^-3 grams per cubic centimeter. How is this number written in standard form
Answers
Answer:
The density of oxygen in standard form is 0.001429 grams per cubic centimeter.
A quadratic equation, y = ax^2 - 6x + 10, has exactly one real root. Calculate the value of a.
Answers
Answer:
a = 0.9
Step-by-step explanation:
For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.
For the given equation:
\(y = ax^2 - 6x + 10\),
• a = a
• b = -6
• c = 10.
Substituting these values into the formula for discriminant, we get:
\((-6)^2 - 4(a)(10) = 0\)
⇒ \(36 - 40a = 0\)
⇒ \(36 = 40a\)
⇒ \(a = \frac{36}{40}\)
⇒ \(a = \bf 0.9\)
Therefore the value of a is 0.9 when the given quadratic has exactly one root.
Find the inverse of A = 9, -2 -10, 7 , if it exists.
Answers
The inverse of matrix A, if it exists, is:
A^(-1) = [7/43, 2/43; 10/43, 9/43]
To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.
Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:
det(A) = (9 * 7) - (-2 * -10)
= 63 - 20
= 43
Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.
The formula to calculate the inverse of a 2x2 matrix is:
A^(-1) = (1/det(A)) * [d, -b; -c, a]
Plugging in the values from matrix A and the determinant, we have:
A^(-1) = (1/43) * [7, 2; 10, 9]
Simplifying further, we get:
A^(-1) = [7/43, 2/43; 10/43, 9/43].
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HELP!! Find the value of x in the triangle!! 20PTS!!
Answers
Answer:
x = 5°
Step-by-step explanation:
We know that in a triangle, the measure of an exterior angle is equal to the sum of its two remote interior angles, therefore:
7x + 4 + 61 = 20x
7x + 65 = 20x
13x = 65
x = 5°
Answer:
Solution given:
61°+(7x+4)°=20x [ exterior angle is equal to the sum of two opposite interior angle]
65+7x=20x
65=20x-7x
13x=65°
x=\( \frac{65}{13} \)=5°
value of x=5°
Given that G=ab find the percentage increase in G when both a and b
increase by 10%
Answers
The percentage change in G is 21 %
What is Percentage change ?Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.
It is given that
G = ab
when a is increased by 10% the new a will be = 1.1 a
When b is increased by 10% the new b will be 1.1 b
So,
G' = 1.1a *1.1 b
G' = 1.21 ab
G' = 1.21
(G' - G)*100/G = (1.21-1)*100/1
The percentage change is 21 %
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Pleaseeee I’m on a timerrrrrrrr
Answers
Answer:
D
Step-by-step explanation:
No need
select the correct answer(click the photo)
Answers
Answer:
B.
General Formulas and Concepts:
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define function
f(x) = 8x + 4
Step 2: Prep
Rewrite: y = 8x + 4Swap x and y: x = 8y + 4Step 3: Find Inverse (Solve for y)
Subtract 4 on both sides: x - 4 = 8yDivide both sides by 8: (x - 4)/8 = yRewrite: y = (x - 4)/8Rewrite: f⁻¹(x) = (x - 4)/8If f(1) = 9 and f(n) = -4f(n-1) + 4 then find the value of f(3).
Answers
Answer:
132
Step-by-step explanation:
f(1) = 9
f(n) = -4f(n-1) + 4
Let n = 2
f(2) = -4f(2-1) + 4 = -4 f(1) +4 = -4(9) +4 = -36+4 = -32
Let n = 3
f(3) = -4f(2-1) + 4 =-4f(2)+4 = -4 (-32) +4 = 128+4=132
Molly works at an electronics store. Her last customer purchased a DVD player for $67.43 and five DVDs for $57.50, including taxes. If the customer paid her with two $100 bills, how much change should she give him?
A.
$75.07
B.
$132.57
C.
$66.27
D.
$142.50
Answers
help ASAP DUE in 10 minutes do not spam or you will get reported A farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape. He decides to add 5.7 yards of fencing to the width of the pen, but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Answers
Answer:
The one you have selected is correct. 9.5(w+5.7)=77.9
Step-by-step explanation:
Area is length x width, but the length is the same. So, the 9.5 is not in the parentheses. The existing width (w) is having 5.7 yards added on before being multiplied for area calculations. Because of the order of operations, (w+5.7) must be in parentheses so it is done before multiplication.
Answer:
9.5(w+5.7)=77.9
Step-by-step explanation:
took the test
Which of the following shows the correct solution steps and solution to 2×+ 7 = -11?
Answers
Answer:
x = - 9
Step-by-step explanation:
2x + 7 = - 11 ( subtract 7 from both sides )
2x = - 18 ( divide both sides by 2 )
x = - 9
The answer is:
x = -9
Work/explanation:
The point of equations is to find the variable's value by isolating it step-by-step.
For this equation, the variable is x.
To isolate it, I will perform a few operations.
First, I will subtract 7 from each side:
\(\sf{2x+7=-11}\)
\(\sf{2x=-11-7}\)
\(\sf{2x=-18}\)
Divide each side by 2
\(\sf{x=-9}\)
Hence, x = -9.
\(\rule{350}{4}\)
Which equation can be used to determine the distance between the origin and (–2, –4)? d = StartRoot ((0 minus 2) + (0 minus 4)) squared EndRoot d = StartRoot (0 minus (negative 2)) squared + (0 minus (negative 4)) squared EndRoot d = StartRoot ((0 minus 2) minus (0 minus 4)) squared EndRoot d = StartRoot (0 minus (negative 2)) squared minus (0 minus (negative 4)) squared EndRoot
Answers
Answer:person up top is right it’s B
Step-by-step explanation: on edg 2020
Answer:
The answer is B
Step-by-step explanation:
lol yw guys
Find the area of all shaded regions. Give your answer as a completely simplified exact value in terms of pi. (no approximations) WHO EVER ANSWERS FIRST GETS 100 BRAINLY POINTS
Answers
Answer:
18 π cm^2.Step-by-step explanation:
The area of the whole circle = π r^2 = 81π cm^2.Since there are 360 degrees in a circle the area of the shaded region = 80/360 * area of the circle.
This = 80/360 * 81 π
= 2/9 * 81 π
= 18 π
hope it helps<3Answer:
Area = 18π cm²
Step-by-step explanation:
The shaded region is a sector of a circle with radius 9 cm.
\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)
From inspection of the give diagram:
θ = 80°r = 9 cmSubstitute the values into the formula for area of a sector:
\(\implies A=\left(\dfrac{80^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2\)
\(\implies A=\dfrac{2}{9} \pi \cdot 81\)
\(\implies A=\dfrac{162}{9} \pi\)
\(\implies A=18 \pi\;\; \f cm^2\)
Therefore, the area of the shaded region is 18π cm².